HeckeCharValuesGood( HW, w )
Let HW be a Hecke algebra for the Coxeter group CoxeterGroup(HW),
let w be a good element of CoxeterGroup(HW) in the sense of
GM97, and let d be the order of w.
HeckeCharValuesGood computes the values of the irreducible characters
of the Iwahori-Hecke algebra HW on T_w^d. The point is that the
character table of the Hecke algebra is not used, and that all the
eigenvalues of T_w^d are monomials in HW.parameters, so this can be
used to find the absolute value of the eigenvalues of T_w, a step
towards computing the character table of the Hecke algebra.
We continue the example in HeckeCentralMonomial:
gap> HeckeCharValuesGood( H, [ 1, 2, 3 ] );
[ v^0, v^60, 5*v^24, 5*v^36, 3*v^20, 3*v^20, 3*v^40, 3*v^40, 4*v^30,
4*v^30 ]
This function requires the package "chevie" (see RequirePackage).
Previous Up Top
Index
GAP 3.4.4